Finite Group Databasebeta

← #13074276

Subgroups — #13074276

Order 1408.

444 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#393C211yesmaximal, characteristic
2#10622843C212yesmaximal, complemented
3#10622562C212yesmaximal
4#10622560C211yesmaximal, characteristic
5#10622556C211yesmaximal, characteristic
6C22⋊C4×Dic11C212yesmaximal
7#10622266C212yesmaximal, complemented
8#10622265C212yesmaximal, complemented
9#10622259C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C23×Dic11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2212yes—
21C2×C4×Dic11C2212yes—
22C11×#95C2212yes—
23C11×#95C2211yescharacteristic
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C2×Q8×C11—24no—
33C2×Q8×C11—41no—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2312yes—
38C22×Dic11—41no—
39C22×Dic11—41no—
40C22×Dic11Q814yescomplemented
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C2×Dic22—24no—
46C2×Dic22—41no—
47C11×C22⋊C4—24no—
48C11×C22⋊C4—41no—
49C22⋊Dic11—24no—
50C22⋊Dic11—41no—
51C4⋊Dic11—24no—
52Dic11⋊C4—24no—
53Dic11⋊C4—42no—
54C4×Dic11—42no—
55C4×Dic11—42no—
56#2607—111nomaximal, Sylow
57C23×C11—22no—
58C23×C11—22no—
59C23×C11—21no—
60C23×C11—21no—
61C23×C11C2×Q812yes—
62C23×C11C2411yescharacteristic
63Q8×C11—44no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11#4114yes—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—44no—
85C2×Dic11C2×Q814yes—
86C2×Dic11#4114yes—
87Dic22—44no—
88#399—112no—
89#393—111no—
90#393D1111yescharacteristic
91#391—112no—
92#391—112no—
93#387—112no—
94#387—112no—
95#381—111no—
96C4×C22⋊C4—112no—
97C22×C11—24no—
98C22×C11—22no—
99C22×C11—41no—
100C22×C11—41no—
101C22×C11—42no—
102C22×C11C22×Q811yescharacteristic
103C22×C11C2×#4112yes—
104C22×C11C2×#4112yes—
105C22×C11H(5,𝔽2)11yescharacteristic
106C22×C11H(5,𝔽2)11yescharacteristic
107C4×C11—24no—
108C4×C11—41no—
109C4×C11—41no—
110C4×C11—42no—
111Dic11—24no—
112Dic11—24no—
113Dic11—42no—
114Dic11—42no—
115C22×Q8—111no—
116C22×Q8C2×D1111yescharacteristic
117C23×C4—111no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—112no—
121C2×C22⋊C4—112no—
122C2×C22⋊C4—111no—
123C2×C22⋊C4C2×D1112yes—
124C2×C22⋊C4C2×D1111yescharacteristic
125C2×C42—112no—
126C2×C42—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95—112no—
131#95—111no—
132#95—112no—
133#95—112no—
134#95C2×D1111yescharacteristic
135#95C2×D1112yes—
136C2×C11—42no—
137C2×C11#53312yes—
138C2×C11#54311yescharacteristic
139C2×C11#55111yescharacteristic
140C2×C11#55111yescharacteristic
141C2×C11#55912yes—
142C24C22×D1111yescharacteristic
143C2×Q8—24no—
144C2×Q8—41no—
145C2×Q8—224no—
146C2×Q8—441no—
147C22×C4—112no—
148C22×C4—112no—
149C22×C4—114no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4—441no—
153C22×C4—441no—
154C22×C4C22×D1111yescharacteristic
155C22×C4C22×D1111yescharacteristic
156C22×C4C22×D1112yes—
157C22×C4C22×D1112yes—
158C4⋊C4—224no—
159C4⋊C4—224no—
160C4⋊C4—442no—
161C22⋊C4—24no—
162C22⋊C4—41no—
163C22⋊C4—224no—
164C22⋊C4—441no—
165C42—442no—
166C42—442no—
167C11#260711yescharacteristic, complemented, Sylow
168C23—22no—
169C23—21no—
170C23—22no—
171C23—21no—
172C23Q8×D1112yes—
173C23C23×D1111yescharacteristic
174Q8—44no—
175Q8—444no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—114no—
186C2×C4—114no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—444no—
198C2×C4#434114yes—
199C22—24no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—42no—
204C22C2×#434112yes—
205C22#6703711yescharacteristic
206C22C2×Q8×D1111yescharacteristic
207C22#41×D1112yes—
208C22#6704211yescharacteristic
209C4—24no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—224no—
214C4—224no—
215C4—442no—
216C4—442no—
217C2—42no—
218C2#1062311811yescharacteristic
219C2#1062315312yes—
220C2#1062316511yescharacteristic
221C2#1062321011yescharacteristic
222C2#1062321212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×C11C23
hypercenter#393D11
hypocenterC11#2607
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10622843C2semidirect
7. #10622266C2semidirect
8. #10622265C2semidirect
9. #10622259C2semidirect
40. C22×Dic11Q8semidirect
167. C11#2607semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#3932
#106228432
#106225622
#106225602
#106225562
C22⋊C4×Dic112
#106222662
#106222652
#106222592
#260711